|Don't ask to ask, just ask|
I'll probably get bashed for this, but if you are looking to learn a *nix with a Windows background, try FreeBSD. I did it that way.
The reason I say this is because FreeBSD is not as install friendly as RedHate and most of its brothers, it takes time and effort to do the install the first time, and X Windows can be a chore.
Now people are looking at this going, "You idiot, why would you recommend the harder route?" Easy answer, you will know a whole lot more about the FreeBSD (and other *nix types) after that installation than you will after doing the point and click install of RedHate. You will understand the file system better, understand how X Windows is working better, and understand the mentality behind *nix a bit better (i.e.: Multi-User vs. Single-User, and RedHate is really going for the single user look and feel).
The other reason for FreeBSD is your comment: "I enjoy getting my applications and just running "setup" to install them." The FreeBSD ports directory is arguably the closest thing to this on the *nix platform. Certainly easier than RPMs, and although I have heard good things about Debians Package manager, I don't know it well enough to compare it.
This is not going to be an easy route, some of the things you take for granted in Windows are just not going to be there. But you will also start to find (later down the road) that the *nix platforms have some versatilities that Windows doesn't have. You will need to go much deeper than the UI to find this as the UI's in *nix are not nearly as stable and robust as Windows. They are coming along, but they are not quite there yet. But then again, if you are any good with Windows at all, you already know that the commandline is the only place to get any real work done, even in Windows.
Good Luck, and I hope you manage to come out of it with respect for all operating systems rather than becoming a zealous convert. I currently run 5-7 different OS's for a variety of different things and each one of them does excel at certain things, even my RedHate box :)
"Nothing is sure but death and taxes" I say combine the two and its death to all taxes!